The invention relates to an oscillation damper comprising a cylinder with an axis, a piston rod axially movably guided through at least one cylinder end, a piston connected to the piston rod inside the cylinder, a plurality of fluid chambers having capacities which are variable relative to one another as a function of the movement of the piston rod relative to the cylinder and fluid connections between fluid chambers, wherein in at least one fluid connection, and more particularly in a fluid connection which is provided on the cylinder, there is provided a shut-off valve component, and more particularly a shut-off valve component fixed with respect to said cylinder, between two portions of this fluid connection, wherein moreover the shut-off valve component is constructed with at least one valve seat to which a first portion is attached, wherein moreover a first side of the valve shut-off element can be elastically pressed against the valve seat while shutting off the first portion, wherein moreover a second side of the valve shut-off element, which is remote from the first side, of the valve shut-off element can be loaded adjacently to a control chamber by the fluid pressure in this control chamber, wherein moreover the control chamber is attached via a throttle section passing through the valve shut-off element to the first portion, wherein moreover the control chamber communicates via a control chamber outlet with the second portion and wherein this control chamber outlet is allocated an outlet cross section dimensioning device.